A363222 - OEIS

A363222

Numbers whose multiset of prime indices satisfies (maximum) - (minimum) = (length).

10, 21, 28, 42, 55, 70, 88, 91, 98, 99, 132, 165, 187, 198, 208, 220, 231, 247, 308, 312, 325, 330, 351, 363, 391, 455, 462, 468, 484, 520, 544, 550, 551, 585, 702, 713, 715, 726, 728, 770, 780, 816, 819, 833, 845, 975, 1073, 1078, 1092, 1144, 1170, 1210, 1216

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OFFSET

1,1

COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=1..53.

FORMULA

A061395(a(n)) - A055396(a(n)) = A001222(a(n)).

EXAMPLE

The terms together with their prime indices begin:

10: {1,3}

21: {2,4}

28: {1,1,4}

42: {1,2,4}

55: {3,5}

70: {1,3,4}

88: {1,1,1,5}

91: {4,6}

98: {1,4,4}

99: {2,2,5}

132: {1,1,2,5}

165: {2,3,5}

187: {5,7}

198: {1,2,2,5}

MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[100], Max@@prix[#]-Min@@prix[#]==Length[prix[#]]&]

CROSSREFS

The RHS is A001222.

Partitions of this type are counted by A237832.

The LHS (maximum minus minimum) is A243055.

A001221 (omega) counts distinct prime factors.

A112798 lists prime indices, sum A056239.

A360005 gives median of prime indices, distinct A360457.

Cf. A067801, A111907, A118096, A237821, A361205, A361908, A361909.

Sequence in context: A353402 A353432 A331997 * A242287 A165403 A097386

Adjacent sequences: A363219 A363220 A363221 * A363223 A363224 A363225

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 29 2023

STATUS

approved